A wide variety of data storage devices are used today. Some examples include magnetic recording devices such as hard disk drives (HDD) and digital linear tapes (DLT), and optical storage devices such as compact disks (CD) and digital versatile disks (DVD). Based on the developments of the atomic force microscope (AFM), new probe based storage concepts have been introduced over the past few years. Probes having a nanoscale tip have been used for modifying the topography and for scanning an appropriate storage medium. Data are written as sequences of symbols represented by topographical marks, such as indentation marks and non-indentation marks. The tips comprise apexes with a radius in the nanometer range, and the indentation marks have a comparable diameter, for example, a diameter in the range of 20 to 30 nm or even smaller. Hence, these data storage concepts promise ultra-high storage area density.
A storage device for storing data based on the AFM principle is disclosed in “The millipede—more than 1,000 tips for future AFM data storage” by P. Vettiger et al., IBM Journal Research Development, Vol. 44, No. 3, March 2000. The storage device has a read function and a write function based on the mechanical scanning of a storage medium with an array of probes each having a tip. For this purpose, the probes comprise cantilevers that carry the sharp tips on their end sections. Symbols are represented by indentation marks and non-indentation marks in a polymer layer. The probes respond to these topographic changes while they scan the surface of the polymer medium.
Indentation marks are formed on the polymer medium by thermomechanical recording. Writing of an indentation mark is achieved by applying a voltage pulse across two of the cantilever terminals to heat a write heater and tip and, simultaneously, another voltage pulse to the substrate of the polymer medium to create a local force between tip and medium. As a result, a nanometer-sized indentation is formed on the medium, representing an encoded ‘1’ symbol. The absence of an indentation at the position of a topographical mark represents an encoded ‘0’ symbol.
Reading is also accomplished by a thermomechanical concept. A voltage is applied across two of the cantilever terminals, so that a read heater heats up to a temperature that is not high enough to soften the polymer layer as is necessary for writing. The thermal sensing is based on the fact that the thermal conductance between the probe and the storage medium changes when the probe tip is moving in an indentation, as the heat transport is in this case more efficient. As a consequence of this, the temperature of the cantilever decreases and hence also its resistance decreases. This change of resistance is then measured and determines the read-back signal. Reading and also writing the marks is accomplished by moving each probe relative to the storage medium along a line representing a track. The amplitude of a read-back signal is defined as the difference in magnitude between a read-back signal sample that is obtained when the tip of the probe is exactly at an indentation center, and a sample obtained when the tip of the probe is at an indentation-free area of the storage medium, while the probe moves along a track center line. This is also disclosed in “Millipede—a MEMS based Scanning-Probe Data-Storage System”, by E. Eleftheriou et al., IEEE Transactions on Magnetics 39(2), March 2003, pp. 938-945, and in “Signal Processing for Probe Storage,” by H. Pozidis et al., Proceedings of International Conference on Acoustics, Speech and Signal Processing, Philadelphia, Pa., Mar. 19-23, 2005, pp. 745-748.
The reliability of data retrieval in data storage devices may be improved by employing modulation codes to constrain the sequences that are written on the storage medium. The most popular modulation codes used in conventional data storage devices are the run length limited (RLL) codes. RLL codes are characterized by two parameters, d and k, whereby ‘1’ symbols are constrained to be separated by at least d and at most k ‘0’ symbols. It is customary to refer to RLL codes as (d, k)-constrained codes. Writing at least d ‘0’s between ‘1’s allows to increase the linear recording density by mitigating intersymbol interference, whereas limiting to k the maximum number of consecutive ‘0’s ensures that feedback is provided sufficiently often for timing recovery and gain control loops.
Further, the process of recording and subsequent retrieval of data is likely to introduce errors in the recovered data. These errors are typically related to electronics noise, imperfections in the storage medium surface, and non-ideal recovery of channel parameters during the write and read processes. Errors in the recovered data are corrected using error-correcting codes (ECC). Error-correcting codes add redundancy to the information bits during the encoding operation. This redundancy can be used to correct errors in the recovered data during read operations. Some commonly used ECC for data storage applications are the low-density parity-check (LDPC) codes and the Reed-Solomon (RS) codes. Various decoding algorithms for LDPC codes for practical implementations are known. One such decoding algorithm is disclosed in “Reduced-Complexity Decoding of LDPC Codes”, by J. Chen et al., IEEE Transactions on Communications 53(8), August 2005, pp. 1288-1299. To enhance error-correction capabilities and capacity of the device, ECC is usually implemented jointly with data interleaving and RLL (d,k) coding. In this case it is customary to refer to the ECC as the outer code and to the RLL code as the inner code. The data-retrieval process involves making binary hard (threshold) decisions on the read-back channel-output signals, using the detected binary symbols to decode the (d,k) sequences, deinterleaving the (d,k)-decoder binary output symbols to get channel-output codewords for error-correction, and finally decoding the codewords to retrieve the user information bits.
Besides electronics noise and media noise, other impairments that are present in the read-back signal of a recording channel are, for example, random fluctuations of the read-back signal amplitude, and direct-current (DC) offset of the read-back signal. Further, random fluctuations of the time instants at which pulses are applied for writing information on the storage medium, or at which sampling of the read-back signal for conversion from the analog domain to the digital domain takes place, further impair the quality of the read-back signal. The phenomenon of random fluctuations in the timing of the write and read processes is usually known as jitter. In the data-retrieval process described above, making binary hard decisions leads to non-recoverable loss of information. Moreover, hard-decision decoding of the RLL (d, k) sequences introduces error propagation. Furthermore, a hard-decision scheme does not allow iterative soft decoding of an outer error-correcting code. However, conventional soft decoding techniques, as for example proposed for modulation codes in HDD, do not take into account in the decoding process the presence of such channel impairments as jitter, gain fluctuations, offsets, and nonlinear distortion. Timing recovery, gain adjustment, and offset compensation are performed prior to decoding, and the statistical description of related read-back channel impairments is not exploited. A further drawback of the conventional schemes when applied to a probe storage device is that, in the presence of channel impairments such as random variations in read-back signal amplitude, random variations in sampling instants (jitter), and residual DC offset, the probability of a binary decision error when reading a ‘1’ may be significantly larger than the probability of a binary decision error when reading a ‘0’.
Thus, there is a need for a decoder for the inner code, to obtain near-optimum soft decoding in the presence of random channel impairments without increasing the number of states in the inner decoder, and hence without increasing decoder complexity.